(Disclosure: I have a medical degree -- I am not currently practicing. I am going to take a different path. I don't claim to be an expert on this matter. So this is not "medical advice" per se.)
The difference probably has to do with the amount of heel lift in the various shoes. The angles are not always obvious just looking at the shoe. Boot also could be exerting pressure where the tendon inserts on the bone.
I had Achilles tendonitis at one point. The doctor, a real Texan told me 3 weeks in a walking cast (in which the heel would be lifted, of course) or 3 weeks in cowboy boots. My understanding is that raising the heel a bit, takes some of the tension off the tendon.
If it hurts, don't do it. Be thankful that you have some shoes that don't hurt. Such inflammation can really drag on. Stay out of the boots that hurt! You may have some luck wrapping a single piece of tape around the ankle about two inches above the malleoli (the prominences on either side of the ankle). Could make it feel worse -- then don't do it.
I am assuming this is an overuse/unaccustomed activity type injury -- not sudden pop? If there was a sudden pop and "give", you need an ortho consult and an mri. should repair be necessary, it is much more successful when done sooner rather than later. My personal philosophy these days is NOT to see an orthopedic surgeon unless I am considering an operation or feel something go or break. MRI is a very sensitive test -- if you've got a sore tendon, the MRI IS going to show inflammation. So what. You get a bill and some Aleve and some exercises that you could have looked up on the internet. If you have a great health plan, and you got an afternoon to wait around, I suppose why not.
Judicious use of NSAID (Aleve, ibuprofen, etc -- if they don't seem to help, stop taking them -- not worth the risk to the kidney if you aren't getting benefit), ice/heat combos, stretch after heat -- most people can stretch their Achilles by standing with the heel hanging off a stair -- you can bend the knee ever so slightly to see if this increases the stretch. If you are too flexible to get much of a stretch from this, let me know as I have some other ideas. DO NOT attempt to strengthen the calf with heel raises -- this will only fuel the fire. Maybe after things settle down.
Some doctors will give a hydrocortisone shot for this but there is often hesitation to inject the Achilles so that you can go run around on it. There is some risk of weakening the tendon and making it more vulnerable.
If you have taken a fluoroqunilone antibiotic (they end in -floxacin) in recent months, see a doctor immediately. These drugs have FDA black boxes re: Achilles tendonitis/rupture as they weaken the attachment of the tendon.